Realizability for Peano Arithmetic with Winning Conditions in HON Games

Valentin Blot (1)

1 LIP - Laboratoire de l'Informatique du Parallélisme

We build a realizability model for Peano arithmetic based on winning conditions for HON games. First we define a notion of winning strategies on arenas equipped with winning conditions. We prove that the interpretation of a classical proof of a formula is a winning strategy on the arena with winning condition corresponding to the formula. Finally we apply this to Peano arithmetic with relativized quantifications and give the example of witness extraction for pi-0-2 formulas.

Mots clés: Classical realizability; Peano arithmetic; Hyland Ong game semantics

Domaines: Logique en informatique [cs.LO]

Valentin Blot. Realizability for Peano Arithmetic with Winning Conditions in HON Games. Typed Lambda Calculi and Applications, Jun 2013, Eindhoven, Netherlands. pp 77-92, ⟨10.1007/978-3-642-38946-7_8⟩. ⟨hal-00793324v3⟩